Kinematics and dynamics of machinery_experiments.pdf

7/29/2019 Kinematics and dynamics of machinery_experiments.pdf

1/47

1

Kinematics and

Dynamics of

Machinery Lab

685/MP/11: Yugal Raj Jain

(9891866644)

658/MP/10: Sanjay Kumar Choudhary

(9555707150)

659/MP/10: Saurabh Krishan

(9717231661)

MPAE 2, Section II, 2nd Year


2/47

2

CONTENTS

S.No. Experiment Page No.

1 To study various inversions of four bar chain 3

2 To trace the Involute gear teeth profile using rackcutter

7

3 By the use of apparatus in the lab, perform thefollowing experiments on Watt governor and obtainthe following graphs:

- Force v/s rotation of radius- Speed v/s sleeve displacement

13

4 To plot d - (follower displacement v/s angle of CAM)

curve for given CAM and follower

17

5 To study gyroscopic behaviour and verify gyroscopiccouple due to load check

23

6 To study the functions of a governor and the plot agraph between force and radius of rotation by using aHartnell Governor

27

7 To study damped and free oscillations of a pendulum;determine the radii of gyration, the time period for abeach ball, a helical spring, a Bi-Filer suspensions, anda compound pendulum, as required.

30

8 To measure co-efficient of friction between pulleymaterial and different belt material and to measurepower transmitted with varied belt tension andplotting a graph of (T1-T2) vs (T1+T2)/2 i.e tensioncharacteristics.

36

9 To determine the torque distribution of epicyclic geartrain and to study the functioning of the handoperated model.

41

10 To study the balancing of rotary masses 45


3/47

3

Experiment 1

Aim: To study various inversions of four bar chain.

Apparatus: Corresponding arrangements for various four bar mechanisms.

Theory: Inversions of mechanisms is the method of obtaining different mechanisms

by fixing different links in a kinematic chain.

1) BEAM ENGINE (CRANK AND LEVER MECHANISM):

In this mechanism, link 2 is the crank and the link 4 is the lever. When the

crank rotated about the fixed centre A, the lever oscillates about a fixed

centre D. The end E of the lever CDE is connected to a piston rod which

reciprocates due to the rotation of the crank. The purpose of this mechanismis to convert rotary motion into reciprocating motion.

Figure: Schematic diagram of beam engine mechanism

Figure: A Beam Engine


4/47

4

2) ACKERMAN STEERING GEAR MECHANISM:

In this mechanism, the two short links AB, CD are equal in length, while the

links AD, BC are unequal in length.

When the cat is moving along a straight path, the mechanism takes up the

position shown at (b) and the proportions of the links are so fixed that the

axes of all four wheels intersect at the same point I. This ensures that the

relative motion between the tyres and the road surface shall be one of pure

rolling.

Here, link 2 and link 4 oscillate and hence this mechanism is called as double

lever mechanism. Link 1 is fixed and the link 3 is a coupler.

Figure: Ackerman steering gear mechanism

Figure: Taking a left turn


5/47

5

3) COUPLING ROD OF LOCOMOTIVE (DOUBLE CRANK MECHANISM):

Coupled wheels of locomotive are example of a double crank mechanism.

This mechanism consists of four links as shown in the figure. Coupled wheels

of locomotive are meant for transmitting rotary motion of one wheel toanother. In this mechanism, the links AB and CD (having equal length) act as

crank and connected to the respective wheels. The link BC acts as a coupling

rod and the link AD is fixed in order to maintain a constant centre to centre

distance between them.

Figure: Coupled wheels of locomotive

4) ELLIPTICAL TRAMMEL (INVERSION OF DOUBLE SLIDER CRANK CHAIN

MECHANISM):

This instrument is used to draw ellipse. Here link 4 is a slotted bar which is

fixed. Link 1 and 3 are known as slider and forms sliding pairs with link 4. Link

2 is a bar which forms turning pair with 1 and 3. When the slider slides along

the groove any point say P on the slider traces an ellipse on the surface of link

4.

A little consideration will show that AP and BP are semi-major and semi-minor

axes respectively.

Figure: Elliptical trammel


6/47

6

Result: The various inversions of thefour bar chain werestudied.

Precautions:

1) Handle the apparatus carefully

2) While studying the inversions, dont move the apparatus too quickly or strongly.

It may foul the apparatus.

Bibliography:

1) http://books.google.co.in/books?id=oCbM7kwNFtIC&pg=PA15&lpg=PA15&dq=beam+an

d+engine+mechanism&source=bl&ots=rmHq6FEEbD&sig=szjESNR0wc8CDiuQdwa5m6Cf

gI4&hl=en&sa=X&ei=BQFjUYHiCM2srAexuYGoCw&sqi=2&redir_esc=y#v=onepage&q=be

am%20and%20engine%20mechanism&f=false

2) http://en.wikipedia.org/wiki/Ackermann_steering_geometry
http://books.google.co.in/books?id=oCbM7kwNFtIC&pg=PA15&lpg=PA15&dq=beam+and+engine+mechanism&source=bl&ots=rmHq6FEEbD&sig=szjESNR0wc8CDiuQdwa5m6CfgI4&hl=en&sa=X&ei=BQFjUYHiCM2srAexuYGoCw&sqi=2&redir_esc=y#v=onepage&q=beam%20and%20engine%20mechanism&f=falsehttp://books.google.co.in/books?id=oCbM7kwNFtIC&pg=PA15&lpg=PA15&dq=beam+and+engine+mechanism&source=bl&ots=rmHq6FEEbD&sig=szjESNR0wc8CDiuQdwa5m6CfgI4&hl=en&sa=X&ei=BQFjUYHiCM2srAexuYGoCw&sqi=2&redir_esc=y#v=onepage&q=beam%20and%20engine%20mechanism&f=falsehttp://books.google.co.in/books?id=oCbM7kwNFtIC&pg=PA15&lpg=PA15&dq=beam+and+engine+mechanism&source=bl&ots=rmHq6FEEbD&sig=szjESNR0wc8CDiuQdwa5m6CfgI4&hl=en&sa=X&ei=BQFjUYHiCM2srAexuYGoCw&sqi=2&redir_esc=y#v=onepage&q=beam%20and%20engine%20mechanism&f=falsehttp://books.google.co.in/books?id=oCbM7kwNFtIC&pg=PA15&lpg=PA15&dq=beam+and+engine+mechanism&source=bl&ots=rmHq6FEEbD&sig=szjESNR0wc8CDiuQdwa5m6CfgI4&hl=en&sa=X&ei=BQFjUYHiCM2srAexuYGoCw&sqi=2&redir_esc=y#v=onepage&q=beam%20and%20engine%20mechanism&f=falsehttp://books.google.co.in/books?id=oCbM7kwNFtIC&pg=PA15&lpg=PA15&dq=beam+and+engine+mechanism&source=bl&ots=rmHq6FEEbD&sig=szjESNR0wc8CDiuQdwa5m6CfgI4&hl=en&sa=X&ei=BQFjUYHiCM2srAexuYGoCw&sqi=2&redir_esc=y#v=onepage&q=beam%20and%20engine%20mechanism&f=falsehttp://books.google.co.in/books?id=oCbM7kwNFtIC&pg=PA15&lpg=PA15&dq=beam+and+engine+mechanism&source=bl&ots=rmHq6FEEbD&sig=szjESNR0wc8CDiuQdwa5m6CfgI4&hl=en&sa=X&ei=BQFjUYHiCM2srAexuYGoCw&sqi=2&redir_esc=y#v=onepage&q=beam%20and%20engine%20mechanism&f=falsehttp://books.google.co.in/books?id=oCbM7kwNFtIC&pg=PA15&lpg=PA15&dq=beam+and+engine+mechanism&source=bl&ots=rmHq6FEEbD&sig=szjESNR0wc8CDiuQdwa5m6CfgI4&hl=en&sa=X&ei=BQFjUYHiCM2srAexuYGoCw&sqi=2&redir_esc=y#v=onepage&q=beam%20and%20engine%20mechanism&f=falsehttp://en.wikipedia.org/wiki/Ackermann_steering_geometryhttp://en.wikipedia.org/wiki/Ackermann_steering_geometryhttp://en.wikipedia.org/wiki/Ackermann_steering_geometryhttp://books.google.co.in/books?id=oCbM7kwNFtIC&pg=PA15&lpg=PA15&dq=beam+and+engine+mechanism&source=bl&ots=rmHq6FEEbD&sig=szjESNR0wc8CDiuQdwa5m6CfgI4&hl=en&sa=X&ei=BQFjUYHiCM2srAexuYGoCw&sqi=2&redir_esc=y#v=onepage&q=beam%20and%20engine%20mechanism&f=falsehttp://books.google.co.in/books?id=oCbM7kwNFtIC&pg=PA15&lpg=PA15&dq=beam+and+engine+mechanism&source=bl&ots=rmHq6FEEbD&sig=szjESNR0wc8CDiuQdwa5m6CfgI4&hl=en&sa=X&ei=BQFjUYHiCM2srAexuYGoCw&sqi=2&redir_esc=y#v=onepage&q=beam%20and%20engine%20mechanism&f=falsehttp://books.google.co.in/books?id=oCbM7kwNFtIC&pg=PA15&lpg=PA15&dq=beam+and+engine+mechanism&source=bl&ots=rmHq6FEEbD&sig=szjESNR0wc8CDiuQdwa5m6CfgI4&hl=en&sa=X&ei=BQFjUYHiCM2srAexuYGoCw&sqi=2&redir_esc=y#v=onepage&q=beam%20and%20engine%20mechanism&f=falsehttp://books.google.co.in/books?id=oCbM7kwNFtIC&pg=PA15&lpg=PA15&dq=beam+and+engine+mechanism&source=bl&ots=rmHq6FEEbD&sig=szjESNR0wc8CDiuQdwa5m6CfgI4&hl=en&sa=X&ei=BQFjUYHiCM2srAexuYGoCw&sqi=2&redir_esc=y#v=onepage&q=beam%20and%20engine%20mechanism&f=false


7/47

7

Experiment 2

Aim: To trace the Involute gear teeth profile using rack cutter

Apparatus: Rack cutter, Plain sheet, Geometry box instruments, 3 polystyrene discs(P.C.D=200,300,450)

Theory:

Figure: General gear nomenclature diagram

IMPORTANT NOMENCLATURE OF GEARS:

Gear, wheel: The larger of two interacting gears or a gear on its own.

Pinion: The smaller of two interacting gears.

Path of contact: Path followed by the point of contact between two meshing gear teeth

Pitch point: Point where the line of action crosses a line joining the two gear axes.

Pitch circle, pitch line: Circle centered on and perpendicular to the axis, and passing

through the pitch point. A predefined diametral position on the gear where the circular

tooth thickness, pressure angle and helix angles are defined.

Pressure angle: The complement of the angle between the direction that the teeth exertforce on each other, and the line joining the centers of the two gears. For involute gears,


8/47

8

the teeth always exert force along the line of action, which, for involute gears, is a

straight line; and thus, for involute gears, the pressure angle is constant

Point of contact: Any point at which two tooth profiles touch each other

Involute:

An involute of a circle is a plane curve generated by a point on a tangent, which rolls on

the circle without slipping or by a point on a taut string which is unwrapped from a reel.

To understand what an involute is, consider a simple cylinder and a string as shown

below. Wrap the string around the cylinder. While maintaining tension on the string,

trace the path that the end of the string makes while un-wrapping it around the cylinder.

This path is an involute curve.

Figure: An Involute Curve

On an involute profile gear tooth, the contact point starts closer to one gear, and as

the gear spins, the contact point moves away from that gear and toward the other. If

you were to follow the contact point, it would describe a straight line that starts near one

gear and ends up near the other. This means that the radius of the contact point gets

larger as the teeth engage.

Figure: An Involute gear teeth profile picture


9/47

9

This given experiment is used to illustrate the process of cutting Involute gear teeth by

use of rack cutter. A gear teeth profile can be traced out on a piece of paper placed

between the disc and the rack cutter. An effect of interference and undercutting can be

observed from the profiles traced.

Figure: Generation of Involute gear profile

Observations:


10/47

10

Roll No: 658/MP/10


11/47

11

Result:

Hence, an Involute gear teeth profile can be generated with the help of use of a rack

cutter.

Precautions:

1) Fumbling of hands while tracing the profile can lead to faulty profiles of the

Involute gear teeth. Care should be taken to avoid improper tracing of the gear

teeth.

2) Handle apparatus carefully.

3) The circumference of the disc should just touch the depth line of the rack cutter

that is marked.

4) The white paper should be adhered to the surface so that the profile can be

traced easily without much movement.

5) Take the beginning and end markings on the rack cutter carefully.

Bibliography:

http://en.wikipedia.org/wiki/Involute_gear

http://gearcutting.blogspot.in/2008/02/comparison-between-involute-and.html

http://en.wikipedia.org/wiki/Gear

Theory of Machines, RS Khurmi and JK Gupta, page 392
http://en.wikipedia.org/wiki/Involute_gearhttp://en.wikipedia.org/wiki/Involute_gearhttp://gearcutting.blogspot.in/2008/02/comparison-between-involute-and.htmlhttp://gearcutting.blogspot.in/2008/02/comparison-between-involute-and.htmlhttp://en.wikipedia.org/wiki/Gearhttp://en.wikipedia.org/wiki/Gearhttp://en.wikipedia.org/wiki/Gearhttp://gearcutting.blogspot.in/2008/02/comparison-between-involute-and.htmlhttp://en.wikipedia.org/wiki/Involute_gear


12/47

12

Experiment 3

Aim: By the use of apparatus in the lab, perform the following experiments on Watt

governor and obtain the following graphs:

1) Force & rotation of radius

2) Speed & sleeve displacement

Apparatus: Speed selector, governor, DC motor, sleeve, V-belt, balls, and weights

Theory: A governor, or speed limiter, is a device used to measure and regulate

the speed of a machine, such as an engine. A classic example is the centrifugal

governor, also known as the Watt or fly-ball governor, which uses weights

mounted on spring-loaded arms to determine how fast a shaft is spinning, and

then uses proportional control to regulate the shaft speed.

Figure: Detailed diagram of a governor

For instance, when the load on the engine increases, its speed decreases, therefore itbecomes necessary to increase the supply of working fluids or vice-versa.

The governor automatically controls the supply of fluids to the engine with varying load

conditions & keeps the main speed within limits. The governors are broadly classified as:

1) Centrifugal governor2) Inertia governor

CENTRIFUGAL GOVERNOR


13/47

13

They are based on balancing of centrifugal force on the rotating balls by equal and

opposite radial force called the controlling force. It consist of 2 balls of equal mass w/c is

driven by the engine through bevel gears. The balls and the sleeve revolve with the

spindle speed & fall when speed decreases. The sleeve is connected with ball crank lever.

The supply of fluid decreases when speed rises & vice-versa. The load on the engine

increases, the engine speed decreases. This operates the throttle valve at the other endof the ball crank lever.

Watt Governor

Figure: A Governor

Its the simplest form of a centrifugal governor. Its a conical pendulum with links

attached to a sleeve of negligible mass. The arms of the governor are connected to the

spindle in the fall way. The point p is the offset from the spindle axis and the arm when

produced nearest to o.

Applications:

It was commonly used to maintain the engines speed of trucks or other vechicles.

It is still use in Ships and trains engine.

They are seen on steam engines, internal combustion engines and variously fueled

turbines

We can use it on ac generators to maintain the electricity supply with the

load increases on it.

Its assumed that the weight of the link, sleeve and arm are negligible as compared to

balls


14/47

14

1) Centrifugal force (Fc) acting on the balls

2) the tension t in the arm

3) weight w of the balls

EMo=0

Fc x h=w*x*r=m*g*r

Mw^2r h=mgr

H=g/w^2

Observations:

WATT GOVERNOR:

Length of link (I) = 125 mm

Mass of each ball= 0.742 kg

Height of governor (h)=ho-x/2

Radius of rotation (r)=100/2+ lsin

Documents

Kinematics and dynamics of machinery_experiments.pdf